One-Parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

Based on the spectral statistics obtained in numerical simulations on three-dimensional disordered systems within the tight-binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary, and symplectic symmetries ( β0ex0ex=0ex0ex1,2,4) onto a single scaling curve. This relation provides strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, Pg(s), is given for each symmetry class β, where g is the dimensionless conductance.